By now we should have grown used to thumb-twiddling in euroland. Even so, the failure of the eurogroup and the International Monetary Fund to reach a deal on Greece's finances is disgraceful.

The basic problem is that the eurozone power group is groping for something that doesn't exist. It wants a financing package that is small enough to maintain the pretence that the last bailout arrangements are proceeding swimmingly; but the ministers also want to make Greek debt sustainable.

It can't be done. The stock of Greek debt is simply too high – as a ratio of GDP, it is forecast to pass 190% in 2014 as recession takes its toll.

The measures under contemplation are essentially tweaks, such as an interest holiday and a €10bn voluntary buy-back at a discount of IOUs held by the private sector. Such actions would chip a few percentage points off the debt-to-GDP ratio but the tower of borrowings would still be daunting. Few people would believe seriously that Greece's debt ratio would fall to 120% by 2020, as originally envisaged, or even by 2022, as EU ministers are now prepared to accept.

The IMF got the correct remedy at the outset of these talks: it's time for so-called official lenders, which would include eurozone countries and the European Central Bank, to accept a haircut on their loans. That's the only way to achieve debt sustainability in Greece definitively.

The IMF's stance provoked an outbreak of heebie-jeebies among EU politicians, who complain variously that a debt write-off would be illegal and would encourage the electorates of Ireland, Spain and Portugal to expect similar relief.

Well, yes, but the risk in failing to confront the Greek crisis is probably worse. As Marc Ostwald of Monument Securities puts it, there are no solutions other than outright default: "This will not change today, on 26 November or any other date, though the longer the various parties involved fail to face up to this reality, the higher the probability of a very disorderly default."

Unfortunately, next Monday (26 November) will probably produce some form of compromise that delays resolution for another year, when Germany's elections are out of the way. But the eurogroup is playing with fire. Every chapter of the eurozone crisis has carried a similar theme: when politicians don't present themselves as serious, markets react badly.